Disclaimer: This document was part of the DSP Solution Challenge 1995 European Team Papers. It may have been written by someone whose native language is not English. TI assumes no liability for the quality of writing and/or the accuracy of the information contained herein. Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP Authors: Vladimir N. Ivanov Arthur A. Lanne Igor V. Moroz Oleg B. Semienov Sergey N. Frolov St. Petersburg State University of Telecommunications Digital Signal Processing Solutions September 1996 SPRA319
Transcript
Disclaimer: This document was part of the DSPSolution Challenge 1995 European Team Papers. Itmay have been written by someone whose nativelanguage is not English. TI assumes no liability for thequality of writing and/or the accuracy of theinformation contained herein.
Implementing Vocoder and HF ModemAlgorithms Using the TMS320C31 DSP
Authors: Vladimir N. IvanovArthur A. LanneIgor V. MorozOleg B. SemienovSergey N. Frolov
St. Petersburg State University ofTelecommunications
Digital Signal Processing Solutions September 1996 SPRA319
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ContentsAbstract ........................................................................................................................... 7Product Support on the World Wide Web .................................................................... 8Introduction..................................................................................................................... 9Universal DSP Module.................................................................................................. 10Vocoders ....................................................................................................................... 12
Determination of the Spectral Parameter.................................................................. 12Peculiarities of Speech Coding Algorithms at 2.4 and 1.2 kb/s ................................ 15
High Frequency Modem ............................................................................................... 16Reed-Solomon Code ................................................................................................ 21Convolution Coding .................................................................................................. 21Trellis Coding............................................................................................................ 21
FiguresFigure 1. Functional Scheme........................................................................................... 10Figure 2. Demodulator Block Diagram............................................................................. 16Figure 3. Average Conditions .......................................................................................... 19Figure 4. Bad Conditions ................................................................................................. 20
Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP 7
Implementing Vocoder and HFModem Algorithms Using the
TMS320C31 DSP
Abstract
This application report describes the implementation of a universalDSP module (UDM) to vocoders for a range of bit rates and tomodems operating in the voice-band range. The UDM is based onthe Texas Instruments (TI™) TMS320C31 DSP.
Difficulties in vocoder design are examined as well asmeasurement results for the HF modem under simulated HFchannel environments. The error correction coding is variedamong several methods during the HF modem measurement.
A functional description of the DSP module is included. Thedesign described in this project enables the system to supportvocoders with a bit rate range of 1.2 to 32 kb/s and HF modemswith a bit rate range of 1.2 to 4.8 kb/s. An effective method oflinear prediction parameter evaluation is presented for the bit raterange of 1.2 to 4.8 kb/s.
Parallel HF modem functionality and experimental researchresults on HF channel characteristics are also presented. The HFchannel is simulated in real time using the PC-plugged DSPmodule. The fast synchronization approach is applied to a realworld signal with a large frequency offset. Various methods ofcoding are compared.
This document was part of the first European DSP Education andResearch Conference that took place September 26 and 27, 1996in Paris. For information on how TI encourages students fromaround the world to find innovative ways to use DSPs, see TI’sWorld Wide Web site at www.ti.com.
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8 Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP
Product Support on the World Wide Web
Our World Wide Web site at www.ti.com contains the most up todate product information, revisions, and additions. Usersregistering with TI&ME can build custom information pages andreceive new product updates automatically via email.
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Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP 9
Introduction
Digital signal processors – effective means for realization oftelecommunications devices in baseband frequency range. Themost used among such devices - vocoders for speechcompression and modems for digital data transmission overcommunications channels. General in realization of these devicesis the presence of the analog-digital interface from one end anddigital – with other. It lets to build both types of devices on thesame hardware platform. At development of such platform it isnecessary to take into account specific peculiarities of vocodersand modems in a part of tuning under clock frequencies of digitaldata receiving and transmitting.
In the section, Universal DSP Module, of the present article afunctional scheme of the universal DSP module is described onthe basis of which a number of vocoders in a rage of bit rates 1.2and 32kbit/s and HF modem on bit rates of 1.2 and 4.8 kbit/s arerealized.
In the section, Vocoders, some peculiarities of vocodersalgorithms are stated. In particular for rates 1.2 to 4.8 kbit/s aneffective method of linear prediction parameters evaluation isoffered.
In the section, High Frequency Modem, bases of the parallel HFmodem functioning and results of an experimental research of itscharacteristics over HF channel are stated. HF channel issimulated in real time using the PC-plugged DSP module. The fastsynchronization approach is offered using the working signal inconditions of a large frequency offset. Various methods of codingare compared.
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10 Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP
Universal DSP Module
The functional scheme of the module is submitted on Figure 1. Itconsists of
q TMS320C31PQL50 DSP with external 8-bit ROM (256K) and32K or 128K of flash memory
q Analog/digital interface contained in the TLC3204X integratedcircuit (IC)
q Control and interface logic block contained in the Xilinx’sXC3030A FPGA IC
q Microcontroller (MC) TMS370C710
q Some standard interface logic ICs used for control signals forthe DSP and memory
Figure 1. Functional Scheme
The process of module initialization can be shared into threestages:
q XC3030A initialization (configuration block is loaded from aflash memory over 8 bit data bus)
q Boot load of the program for the TMS320C31 DSP
q Initialization of the TLC3204X over the serial port of the DSP
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Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP 11
The FPGA IC is intended for:
q Creates bi-directional 8 bit data bus between DSP and MC
q Creates 8 bit control channel (8 inputs and 8 outputs)
q Creates various control signals for the DSP and for the MC
The TMS370C710 MC lets to realize the interface RS-232 or anyother interface for communication with external devices. MainDSP feature is an opportunity of independent control of ADC andDAC sampling frequencies. It is often necessary for realizationmomem PLL or tuning under colck frequencies, specifying avocoder bit rate. Such opportunity is provided at the expense ofdigital phase detector (PD) design on base FPGA logic. Harmonic(subharmonic) frequencies of master clock TLC and clockfrequencies determining receiving(transmitting) rates should befed to the inputs of PD. Phase detector gives out logic 0 or 1. Itdepends on sign of deviation of these frequencies from eachother.
This information is transmitted to DSP using one least significantbit (if it necessary to change a sampling frequency only ADC orDAC) or two least significant bits (if it necessary to change asampling frequency as ADC and DAC) over 8-bit data busbetween DSP and MC. The other 6 or 7 bits are used asinformation bits. The least significant bits are masked by DSP andused for control of sampling frequencies of ADC and DAC byloading of corresponding factors to the factors into theTLC3204X’s control registers. Average sampling frequency will befollowed to external frequency changes (for example to clockfrequency, determining receiving of the digital information). Forexample there is 16 kHz clock frequency from external DCE(modem) in receiving mode of 16 kbit/s vocoder. This frequency ischanged in result of the modem PLL working. Hence the DACsampling frequency of a vocoder with nominal value 8 kHz alsoshould be changed using above mentioned technique. There aretwo external sockets on DSP module: for DSP emulation and forloading of FPGA configuration file from PC.
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12 Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP
Vocoders
A set of algorithms realized on the given hardware platform ischosen with a condition of universal character of application of thedeveloped device. On one hand required universalness isdetermined by development of an algorithms and softwaresupporting all accepted ITU recommendations for digital speechcommunications and speech compression: G.726, G.727, G.728.Realizations of two last newest recommendations G.723 andG.729 are now developed. And on other hand the most popularbit rates used in the various applications of telecommunications1.2, 2.4, 4.8, 8, 16, 32 kb/s are supported by this board. Formaintenance of speech coding in a range of bit rates from 8 kbpsand below thee are used original algorithms and standards IS-54,USFS-1016, USFS-1015. We shall describe main peculiarities ofrealized algorithms.
Determination of the Spectral Parameter
At bit rates 1.2, 2.4, 4.8 kb/s the information about a current short-term spectrum envelope of a signal is transmitted with linearspectral frequencies (LSF),1 which determined by roots ofsymmetric and anti-symmetric polynomials
)(zAz (z)A (z)P P(z) -1p
1)-(pp1p
++ +==
)(zAz (z)A (z)Q Q(z) -1p
1)-(pp1p
++ +==
for signal short-term spectrum pole model of a kind
kp
1kk
pp
za1
1
)(A
1(z)H
−
=∑+
==z
where ak = Linear prediction coefficients.
p = Order of model equal to 10 in considered algorithms.
Appropriate polynomials ∑=
=k
0i
1-ik,k zP (z)P and
∑=
=k
0i
1-ik,k zQ (z)Q are determined for all intermediate models of a
degree k ≤ p.
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Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP 13
Split Levinson algorithm,2 determining three-term recursiveprocedure of symmetric and anti-symmetric polynomialscoefficients calculation,
(z)Pz(z))Pz(1 (z)P 1-k-1
kk-1
1k α−+=+ (1)
(z)Qz(z))Qz(1 (z)Q 1-k-1
kk-1
1k β−+== (2)
plays fundamental role in calculations LSF. αk and βk aredetermined by Split Levinson algorithm.2 At the initial conditions:
-110 z1 (z)P 2, (z)P +== (3)
-110 z1 (z)Q 0, (z)Q +== (4)
Further, we shall define scalar product for continuous complexfunctions ϕ and ψ in a kind.
∑= )()( ),( iii iξψξϕωψϕ
Thus, each set n,1,k C, k K=∈ξ and positive numbers ωk
corresponds unique scalar product. Let now },,{ 0 pϕϕ K is finite
family of polynomials corresponding degree and ϕo = 1. For eachabove-stated scalar product it is possible to specify unique familyof polynomials which is orthogonal in this scalar product andsubmitting three-term recurrence relation.3
)(b-)()c-( )( 2-j2
1-j1-jjj ξϕξϕξξϕ = (5)
Each family in turn derivates a tridiagonal symmetric matrix
=
n1-n
1-n
221
11
cb0
b
bcb
00bc
T
LLL
LLLLL
LLLLLL
LLL
LL
Thus this family is a family of characteristic polynomials for amatrix T[3],that is
[ ]ji,jjj T-Edet )( )( ξξχξϕ == (6)
where Ti,j = Main sub-matrix of the order j. Moreover from thetheorem Cauchy about sharing it follows that the polynomialssequence is a sequence of Sturm that is zeroes of the nextpolynomials alternate each other on the unit circle.3
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14 Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP
The inverse is also true just if T is some tridiagonal matrix then itsets some sequence of polynomials being a sequence of Sturmand which in turn determines scalar product in which thissequence is orthogonal.3
We shall show now that polynomials submitting three-termrecurrence of a kind (1) , (2) derives polynomials submitting three-term recurrence of a kind (5) . For this purpose we shall make thefollowing replacement variable
ω2coszzX -1 =+= at z = ejw
Designate now through Hk (x) a function.
(z)PZ1
Z (x)H 1k1-
2k
k ++= (7)
Then it is easy to show that the functions which is determined bythis way satisfies the following recurrence relation.
To similar symmetric case we form family of polynomials
p/2,0,1,k (x),F(x)F~
2kk K==
This family is set in view of initial values (4) by formulas
(x)F~
(x)F~
)2(x(x)F~
2x(x)F~
1(x)F~
2k22k12k1k12k2kk
21
0
−−−−− −−−+=
−+=
=
ββββ
β (14)
Appropriate the tridiagonal matrix will have a kind
−+
−+=′
−−−
−−
20
2
02-
T
p1p2p1p
2p1p
4323
232
ββββββ
βββββββ
LL
LLLL
LLLLL
LLL
LL
(15)
An eigenvalues of a matrix T´ are roots of polynomial(x)F(x)F
~p2/p = and consequently polynomial (z)Q 1p+ too. Thus, it
has been shown that LSF are determined by eigenvalues ofmatrixes (11) and (15) . It should be noticed that as theconsequence from the above-stated reasonings follows additionalproperty of LSF alternateness for the next polynomials of a kind(10) or (14) .
In the practical relation as it is necessary to determine onlyquantizing values of LSF, their search can be organized with thebisection method or with the more effective secant method.However, in the given realization we used the tridiagonal QLalgorithm.3 The quantization of spectral frequencies is carried outon the basis of dynamic programming method.4 56789
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16 Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP
Peculiarities of Speech Coding Algorithms at 2.4 and 1.2 kb/s
Two original algorithms at these bit rates were developed.Classical model in a kind of pole filter excited by pulses and noiselays in a basis for the first. The format of transmitted bit stream inthis case coincides the standard USFS-1015.10 However, it ispossible optionally to use improved algorithm of speechtransmission in which the fifth state of a current signal framedescribing voicing aperiodic frames of speech is entered. Twogains are transmitted instead of one into the bit stream of the fifthstate.
Idea of MBE coder lay in a basis of the second algorithm.11 Asspectral parameters vector quantizing LSF and specialtransformed coded differences between a spectrum and 10thorder pole model in pitch harmonics are transmitted in this case.Except these parameters the gain, pitch and five-band voicinginformation are transmitted. The synthesizer will form syntheticspeech by mixing of appropriate amplitude pitch harmonics andoutput of the forming filter excited by noise. Speech transmissionat 1.2 kbps bit rate is carried out with frame interpolation of themissed frames and application of described algorithms.
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Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP 17
High Frequency Modem
The principles of modem design can be shared into two groups:
Parallel, in which the transfer of information occurs on severalcarriers and serial with one carrier. Advantages and the lacks ofboth principles were repeatedly discussed in the literature and it isdifficult to prefer each of principles. Rather fast changes (fading)of the HF channel characteristics are occurred.
For serial modems complicative methods of adaptive filteringreduce the fading effect. The main condition of successful using ofthese methods is fast convergence of adaptation algorithms. It isnecessary for correct work of filter in conditions of nonstationarity.Recent quantity of works devoted to this question has been muchincreased.12
For appreciable effects, significant computing resources arerequired. The parallel modems are more sready against fading incomparison with serial without complicative adaptive processing atthe expense of presence of a guard interval and long-durationsymbol interval.
In the article parallel modem design is discussed. The structure israther traditional. A sum of M harmonic carriers transfers LM bitsusing 2L - ary DPSK modulation with frequencies
000 k 1),-...(M 1, 0,l where1,k(k ,kf =+= - initial number of a
harmonic; f0 - generating frequency; L - degree of modulation) in afrequency range 0.3+3.4 kHz on a symbol interval
s0sym f
NTT =+= τ (where
00 f
1T = interval orthogonality; τ - guard
interval; fs - sampling frequency).
So a bit rate of modem is LM/Tsym bits per second. The digitalinformation, intended for transferred, is encoded by a errorcorrecting coding. Then it feeds to the modulator. The discussionof methods of error correcting coding and decoding will be spentbelow.
The main problem of the demodulator is reliable receiving of thecoded digital information in conditions of fading, significantfrequency offset (±100 Hz), and additive noise of HF channel.Thus the symbol and carrier synchronizations should be carriedout using only a working signal and in condition of minimal time ofsynchronization.
The generalized block diagram of the demodulator is resulted on aFigure 2.
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18 Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP
Figure 2. Demodulator Block Diagram
SpectralAnalysis
UnitADC
StatisticalProcessing
Unit
FrequencyShiftUnit
PhaseCalculation
Unit
DigitalFlow
RecoveringUnit
Input
LF Signal
Recovered
Digital Flow
Group baseband DPSK signal (low frequency signal) is fed to theinput of ADC. The frequency shift unit implements frequency shiftof group signal in correspondence to frequency offset. The valueof a frequency offset is calculated by the statistical processingunit. At large allowable values of a frequency offset the procedureof carrier recovery will be carried out in three stages which will beexplained below. In the spectral analysis unit a spectrum of asignal is calculated every P samples on carrier frequencies(frequency subchannels) using overlapped time windows withduration equalled T0. Thus spectrum is calculated N/P times persymbol interval. A phase spectrum of received signal is calculatedby the phase calculation unit. Phases are found in every Psamples and transferred to the statistical processing unit
The statistical processing unit solves the following problems:
q Carrier recovery that is reached by determination of afrequency offset, transmitted to the frequency offset unit
q Symbol recovery, reached by determination of a symbolinterval edges
Both these problems are solved simultaneously by search of aminimum of the following functional:
{ }[ ]∑ ∆∆ f)n,(FE mϕ (16)
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Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP 19
where f)n,(m ∆∆ ϕ = deviation of a phase difference in the
neighboring symbol intervals from the nearest permitted value 0,
1-LL
1-L1-L 21)-(2 ..., ,
22 ,
2
πππ in mth frequency sub-channel and nth
time window at a ∆f frequency offset of a group signal ; F{ } -square-law function; E operation of time average.
The functional minimization is carried out as over a frequencyoffset and over a clock interval during a symbol interval. The valueof m in (16) can be equal to M or less. It is up to DSP computingresources and stage of carrier recovery.
At the first stage the rough tuning is occurred with the resolution of
a PLL capture band of fine tuning, equalled )T(2
1f
sym1Lcap +=∆ .
Thus divisible to a capture band ∆f is chosen, ensuring a minimum(16) .
At the second stage, fine-tuning is made by definition ∆f, at whichthe value of { }[ ]∑ ∆∆ f)n,(FE mϕ is close to zero. It is supported by
feedback loop from statistical processing unit to frequency shiftunit.
And at last, at the third stage, minimization of (16) is madeaccurate to the frequency sub-channel. It is necessary when thevalue of frequency offset is more than f0. In this case, calculationof (16) is made using m corresponding to the part of subchannelson edges of a working frequency range.
The described above procedure of synchronization reliably worksin conditions of deep fading and significant noise. The heaviestcomputing expenses arise at the first stage of synchronization,especially if to carry out rough tuning for all possible ∆fsimultaneously to reduce the time of synchronization.
With this purpose fast recurrent algorithms of the spectral analysiswere developed on the basis of Goertzel algorithm withdecimation and Fast Fourier Transform (FFT). The functionalminimization is made by simultaneous calculations (16) for all
possible r∆fcap, where r = 0, 1, 1f
f
cap
0 −∆
.
Further fine tuning and the tuning accurate to the frequency sub-channel (kf0) is carried out in condition of ∆f=r0∆fcap, where r0
ensures a minimum of (16).
It is necessary to notice that the minimization of functional (16)can be replaced by determination of its centre of gravity with someweight function. It allows to decrease an error probability.
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20 Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP
Methods of error correcting coding used in the modem stronglyinfluence to modem performance. In the described modem,various methods of coding were applied to improve the reliabilityof reception in conditions of fading:
q Diversity reception
q Reed-Solomon coding
q Convolution coding with various constraint lengths
q Trellis coding
Criterias for use of these methods were efficiency in conditions offading and limited complexity of realization (1 TMS320C31 DSP).All measurements of an error probability were made in real timewith use of HF channel model and realized on PC plugged boardalso based on the TMS320C31 and TLC3204X.
According to the CCIR recommendations (report 549),13 two typesof HF channel were considered: with average (2 rays, frequencyspread = 0.5 Hz, delay between rays = 1 ms) and bad channel (2rays, frequency spread = 2 Hz, delay between rays = 3 ms)conditions.
Moreover frequency offset and additive Gaussian noise weresimulated. The resulted below curves of errors probability arereceived by measurement of an error probability for average andbad conditions (see Figure 3 and Figure 4). Each point of curve isreceived at transmission sample of 10 millions bit.
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Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP 21
Figure 3. Modem Performance Under Average Conditions
+
Figure 4. Modem Performance Under Bad Conditions
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22 Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP
According to the technical requirements of the described modem,the allowable frequency range is (0.5÷3.0 kHz). It is a little bitnarrowed in comparison with a standard voice-band range.Hence, at f0 =50 Hz the maximum number of subchannels M isequal 47 if allowable frequency offset of (±100 Hz). The number ofinformation bits over the symbol interval is equal to 60 at a bit rateof 2400 bit/s. For the HF channel, L should not be more than 3because of hard propagation conditions. Thus, the maximumredundancy is close to 2, which can be received in view of theabove-stated restrictions.
The various variants of coding were compared among themselvesand with uncoded variant with the signal construction (M = 30, L =2) over HF channel models under above mentioned average andbad conditions. Diversity reception had shown the worseperformance than the reception with error correcting coding. Sowe present measurement results of the last one.
Following variants of coding were investigated:
q Reed-Solomon Code
q Convolution coding
q Trellis coding
A brief description of each coding method follows.
Reed-Solomon Code
The input information was coded by a Reed-Solomon code (12, 8)received by truncation from a code (15, 11) over a Galois field GF(16), with a generating polynomial
103263134 xxxxg(x) αααα +++++++=
where α = primitive element of a field.
Input frame of 60 bits was divided by words of length 30 bits whichwere two zero’s complemented up to 32 bits. Each word isrepresented in 48 bits after coding. Then two added zero bits wereextracted coded words to create two 46 bit words which are fed tothe modulator. Thus the coding was made on a grid of frequenciesusing the signal construction (M = 46, L = 2).
Convolution Coding
The structure of coding was corresponded to structure fromreferences14 with the number of cyclically multiplexed coders.
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Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP 23
2/3-convolution coder was realized. Its constraint length V is equalto 6 and matrix of generating polynomials is:
++++++
+++++1xxx1xxxx
1xxxx1xx23232
23223
And two coder variants were tested for signal constructions (M =30, L = 3) and (M = 45, L = 2).
Trellis Coding
Trellis coding15 was developed with v = 4 on the basis of a signalconstruction (M = 30, L = 3). The structure of coding alsocorresponds the structure from reference14 with the metric forfading channels.
Figure 3 and Figure 4 demonstrate modem performance forvarious variants of coding under following conditions: averageconditions (Figure 3), and bad conditions (Figure 4).
q Curves with an index of 0 correspond to the uncoded variant.
q Curves with an index of 1 correspond to the Reed-Solomoncode.
q Curves with an index of 2 correspond to convolution codingwith a constraint length of v = 6 and signal constructions of(M = 30, L = 3).
q Curves with an index of 3 correspond to trellis-coding.
q Curves with an index of 4 correspond to convolution codingwith a constraint length of v = 6 and signal constructions of(M = 45, L=2).
It is visible that even such simple code as a Reed-Solomon codegives appreciable improvement of the modem performance. Useof a convolution code with a signal construction of (M = 30, L = 3)can give even deterioration of the modem performance (seeFigure 4).
It should be emphasized that use of a more simple Trellis-code (v= 4) with the special metric lets to achieve results not worse thanby use of convolution code with V = 6 and Hamming metric.Presently we try to use more complex Trellis-coding. Neverthelessconvolution code with a constraint length of v =6 and L = 2 (4PSK)shows the minimal error probability among realized variants. It isnecessary to note that reliability of synchronization for L = 3 (8PSK) is worse than at L = 2 (4PSK).
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24 Implementing Vocoder and HF Modem Algorithms Using the TMS320C31 DSP
References
1 S. Saito and K.Nakata, Fundamentals of Speech Signal Processing,Academic press, 1985.
2 P. Delsarte and Y.Genin, "The Split Levinson Algorithm". IEEE Trans.Acoust., Speech and Signal Processing, Vol. ASSP-34.’3,pp.470-478, June 1986.
3 N. Parlett. The Symmetric Eigenvalue Problem, Prentice-Hall, Series incomputational mathematics, 1980.
4 E. Ponomarev, "Methods of Mathematical Representation of LinearSpectrum Frequency", News Institute of RadioElectronics, Vol. 34, No. 12, pp.29-32, December, 1991.
5 ITU Recommendation G.726 - 40,32,24,16 kb/s Adaptive DifferentialPulse Code Modulation (ADPCM). ITU, Geneva. 1990.
6 ITU Recommendation G.727 - 5-, 4-, 3- and 2-Bits Sample EmbeddedAdaptive Differential Pulse Code Modulation (ADPCM).ITU, Geneva, 1990.
7 ITU Recommendation G.728 - Coding of Speech at 16 kb/s Using Low-Delay Code Excited Linear Prediction. ITU, Geneva,1992.
8 ITU Recommendation G.729 - Coding of Speech at 8 kb/s UsingConjugate-Structure Algebraic Code Excited LinearPrediction (CS-ACELP). ITU, Geneva, 1995.
9 ITU Recommendation G.723 - Dual Rate Speech Coder for MultimediaCommunications Transmitting at 5.3 & 6.3 kb/s. ITU,Geneva, 1995.
10 Thomas E. Tremain, "The Government Standard Linear PredictiveCoding Algorithm: LPC-I0", Speech Technology, April,1982, pp.40-49.
11 A.M.Kondoz, Digital Speech: Coding for Low Bit Rate CommunicationsSystems,John Wiley & Sons, 1994.
12 Z. Xiang et. al. “Polynomial Perceptions and Their Applications toFading Channel Equalization and Co-ChannelInterference Suppression”, IEEE Trans. On SignalProcessing, vol.42, No.9, September 1994, pp.2470 -2480.
14 S.C.Cook, M.C.Gill, T.C.Giles " A High-Speed HF Parallel-ToneModem”, “HF Radio Systems and Techniques", 4-7 July1994, Conference Publication, No.392, pp.175-181.
15 G.Ungerboeck “Channel Coding with Multilevel/Phase Signals", IEEETrans. Inf. Theory, vol. IT-28, No. 1, January 1982,pp.55-67.
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